Re: Transfoming probability distributions into fuzzy sets - can anyone help?

Scott Ferson (scott@ramas.com)
Fri, 11 Sep 1998 04:29:18 +0200 (MET DST)

WSiler wrote:

> ...snip...
>
> I can (and often do) characterize that
> same variable as a bell-shaped fuzzy number,
> paramaterized perhaps as central value and
> a hedge "roughly". There is no vagueness
> here, just an uncertainty as to precise
> value. In an expert system, "roughly 2" is
> a heck of a lot more useful than "2 +/- 25%".
>

Yeah, but you need to specify somewhere just what "roughly"
means, don't you? Either explicitly (which is what the
plus-or-minus part does), or through some kind of convention.
Otherwise, we can't specify the fuzzy number to do subsequent
calculations with. So how do you interpret the fuzzy number
"roughly 2"? What does its graph look like?

I assume, by the way, that everyone agrees on a convention
about how to represent "2 +/- 25%" as a fuzzy number. It
should be the triangular fuzzy number whose support is [1.5,
2.5] and whose peak is 2, right? Or is it the trapezoidal
fuzzy number whose support is [1, 3] and whose plateau is
[1.5, 2.5]?

Scott Ferson <scott@ramas.com>
Applied Biomathematics, 516-751-4350, fax -3435

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